Question

If the diagonal of a square is 11.3 meters, approximately what is the perimeter of the square

Answer 1

the length of each side can be found using pythagoras theorem:-

11.3^2 = 2x^2 where x = length od each side
x = sqrt( [11.3^2 / 2)
x = 7.99 meters

Answer 2

The perimeter of the square is
`31.96\ m`

Explanation:

we know that

The perimeter of a square is equal to

`P=4b`

where

b is the length side of the square

Step 1

Find the length side of the square

The diagonal of the square is equal to

Applying the Pythagoras Theorem

`d^(2) =b^(2)+b^(2)\\d^(2)=2b^(2)\\d=b √(2)`

In this problem we have

`d=11.3\ m`

`d=b√(2)` ------> solve for b

`b=d/√(2)`

substitute the value of d

`b=11.3/√(2)\ m`

Step 2

Find the perimeter of the square

`P=4b`

Substitute the value of b

`P=4(11.3/√(2))=31.96\ m`